European patent publication 0,302,045 discloses a two-stroke engine wherein fuel is injected into the combustion chamber in the region of a transfer channel. The injection starts already ahead of the opening of the transfer channel in order to ensure an adequate supply of fuel also at high engine speeds. The combustion air is supplied to the combustion chamber from the crankcase via the transfer channels. The injected fuel quantity is completely transported into the combustion chamber with the combustion air passing from the crankcase. The crankcase must be separately lubricated.